Table A2. Competing model formulations... | Rockefeller University Press

Table A2.

Competing model formulations

Model	Normalized force:	Normalized recruitment term:	Normalized distortion term:	Second order terms:	No. of parameters:
	φ(t) =	$\frac{d ε (t)}{d t} =$	$\frac{d ζ (t)}{d t} =$
I	ε(t)ζ(t)	$- b ε (t) + b [\frac{λ (t) - λ_{d}}{1 - λ_{d}}]$	$- c [ζ (t) - 1] + \frac{1}{υ_{0}} \frac{d λ (t)}{d t}$	—	Three: b and c (with units of s⁻¹) and υ₀ (unit-less)
II	ε(t)ζ(t)	$- (b + γ f (x)) ε (t) + b [\frac{λ (t) - λ_{d}}{1 - λ_{d}}]$	$- c [ζ (t) - 1] + \frac{1}{υ_{0}} \frac{d λ (t)}{d t}$	—	Four: b, γ, and c (with units of s⁻¹) and υ₀ (unit-less)
III	ε(t)ζ(t)	$- b (1 + γ f (x)) ε (t) + b [\frac{λ (t) - λ_{d}}{1 - λ_{d}}]$	$- c (1 + γ f (x)) [ζ (t) - 1] + \frac{1}{υ_{0}} \frac{d l (t)}{d t}$	—	Four: b and c (with units of s⁻¹) and γ and υ₀ (unit-less)
IV	ε(t)ζ(t)	$- (b + γ_{η} f (x)) ε (t) + b [\frac{λ (t) - λ_{d}}{1 - λ_{d}}]$	$- (c + γ_{x} f (x)) [ζ (t) - 1] + \frac{1}{υ_{0}} \frac{d l (t)}{d t}$	—	Five: b and c (with units of s⁻¹) and γ_n, γ_x, and υ₀ (unit-less)
V	ε(t)[ζ(t) + κζ₁(t)]	$- (b + γ f (x)) ε (t) + b [\frac{λ (t) - λ_{d}}{1 - λ_{d}}]$	$- c [ζ (t) - 1] + \frac{1}{υ_{0}} \frac{d λ (t)}{d t}$	$\frac{d ζ_{1} (t)}{d t} = - d ζ_{1} (t) + \frac{1}{υ_{0}} \frac{d λ (t)}{d t}$	Six: b, γ, c, and d (with units of s^-−1) and κ and υ₀ (unit-less)
VI	ε(t)ζ(t)	$- (b + γ f (x)) ε (t) + b [ε_{1} (t)]$	$- c [ζ (t) - 1] + \frac{1}{υ_{0}} \frac{d λ (t)}{d t}$	$\frac{d ε_{1} (t)}{d t} = - a (ε_{1} (t) - \frac{λ (t) - λ_{d}}{1 - λ_{d}} - θ \frac{d λ (t)}{d t})$	Six: b, γ, c, and a (with units of s⁻¹) and θ and υ₀ (unit-less)

Model	Normalized force:	Normalized recruitment term:	Normalized distortion term:	Second order terms:	No. of parameters:
	φ(t) =	$\frac{d ε (t)}{d t} =$	$\frac{d ζ (t)}{d t} =$
I	ε(t)ζ(t)	$- b ε (t) + b [\frac{λ (t) - λ_{d}}{1 - λ_{d}}]$	$- c [ζ (t) - 1] + \frac{1}{υ_{0}} \frac{d λ (t)}{d t}$	—	Three: b and c (with units of s⁻¹) and υ₀ (unit-less)
II	ε(t)ζ(t)	$- (b + γ f (x)) ε (t) + b [\frac{λ (t) - λ_{d}}{1 - λ_{d}}]$	$- c [ζ (t) - 1] + \frac{1}{υ_{0}} \frac{d λ (t)}{d t}$	—	Four: b, γ, and c (with units of s⁻¹) and υ₀ (unit-less)
III	ε(t)ζ(t)	$- b (1 + γ f (x)) ε (t) + b [\frac{λ (t) - λ_{d}}{1 - λ_{d}}]$	$- c (1 + γ f (x)) [ζ (t) - 1] + \frac{1}{υ_{0}} \frac{d l (t)}{d t}$	—	Four: b and c (with units of s⁻¹) and γ and υ₀ (unit-less)
IV	ε(t)ζ(t)	$- (b + γ_{η} f (x)) ε (t) + b [\frac{λ (t) - λ_{d}}{1 - λ_{d}}]$	$- (c + γ_{x} f (x)) [ζ (t) - 1] + \frac{1}{υ_{0}} \frac{d l (t)}{d t}$	—	Five: b and c (with units of s⁻¹) and γ_n, γ_x, and υ₀ (unit-less)
V	ε(t)[ζ(t) + κζ₁(t)]	$- (b + γ f (x)) ε (t) + b [\frac{λ (t) - λ_{d}}{1 - λ_{d}}]$	$- c [ζ (t) - 1] + \frac{1}{υ_{0}} \frac{d λ (t)}{d t}$	$\frac{d ζ_{1} (t)}{d t} = - d ζ_{1} (t) + \frac{1}{υ_{0}} \frac{d λ (t)}{d t}$	Six: b, γ, c, and d (with units of s^-−1) and κ and υ₀ (unit-less)
VI	ε(t)ζ(t)	$- (b + γ f (x)) ε (t) + b [ε_{1} (t)]$	$- c [ζ (t) - 1] + \frac{1}{υ_{0}} \frac{d λ (t)}{d t}$	$\frac{d ε_{1} (t)}{d t} = - a (ε_{1} (t) - \frac{λ (t) - λ_{d}}{1 - λ_{d}} - θ \frac{d λ (t)}{d t})$	Six: b, γ, c, and a (with units of s⁻¹) and θ and υ₀ (unit-less)

Model legend: I, simple RD model; II, RD model with nonlinear interaction term (NLRD model); III, NLRD model with nonlinear distortion effect on distortion (same nonlinear effect of distortion on both recruitment and distortion); IV, NLRD model with nonlinear distortion effect on distortion (same nonlinear effect of distortion on both recruitment and distortion); V, NLRD model with second-order distortion term; VI, NLRD model with second-order recruitment term.

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